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Article Experimental Study and Conjugate Heat Transfer Simulation of Pulsating Flow in Straight and 90◦ Curved Square Pipes

Guanming Guo 1 , Masaya Kamigaki 1, Yuuya Inoue 1, Keiya Nishida 2, Hitoshi Hongou 3, Masanobu Koutoku 3, Ryo Yamamoto 3, Hideaki Yokohata 3, Shinji Sumi 3 and Yoichi Ogata 2,*

1 Graduate School of Engineering, Hiroshima University, Hiroshima 7390046, Japan; [email protected] (G.G.); [email protected] (M.K.); [email protected] (Y.I.) 2 Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima 7390046, Japan; [email protected] 3 Mazda Motor Corporation, Hiroshima 7308670, Japan; [email protected] (H.H.); [email protected] (M.K.); [email protected] (R.Y.); [email protected] (H.Y.); [email protected] (S.S.) * Correspondence: [email protected]

Abstract: The turbulent pulsating flow and heat transfer in straight and 90◦ curved square pipes are investigated in this study. Both experimental temperature field measurements at the cross-sections of the pipes and conjugate heat transfer (CHT) simulation were performed. The steady turbulent flow was investigated and compared to the pulsating flow under the same time-averaged Reynolds number. The time-averaged Reynolds number of the pulsating flow, as well as the steady flow, was



 approximately 60,000. The Womersley number of the pulsating flow was 43.1, corresponding to a 30 Hz pulsating frequency. Meanwhile, the Dean number in the curved pipe was approximately Citation: Guo, G.; Kamigaki, M.; 31,000. The results showed that the local heat flux of the pulsating flow was greater than that of the Inoue, Y.; Nishida, K.; Hongou, H.; steady flow when the location was closer to the upstream pulsation generator. However, the total heat Koutoku, M.; Yamamoto, R.; flux of the pulsating flow was less than that of the steady flow. Moreover, the instantaneous velocity Yokohata, H.; Sumi, S.; Ogata, Y. and temperature fields of the simulation were used to demonstrate the heat transfer mechanism of Experimental Study and Conjugate the pulsating flow. The behaviors, such as the obvious separation between the air and pipe wall, the Heat Transfer Simulation of Pulsating Flow in Straight and 90◦ Curved low-temperature core impingement, and the reverse flow, suppress the heat transfer. Square Pipes. Energies 2021, 14, 3953. https://doi.org/10.3390/en14133953 Keywords: pulsating flow; curved pipe; temperature fields; conjugate heat transfer; local heat transfer

Academic Editor: Gabriela Huminic

Received: 27 May 2021 1. Introduction Accepted: 28 June 2021 Fluid flow and heat transfer in pulsating flows occur in a variety of engineering Published: 1 July 2021 applications, such as reciprocating engines, electronics cooling, and certain heat exchangers. Arterial blood flow is a similar example of such flows. In recent decades, pulsating flow Publisher’s Note: MDPI stays neutral and its heat transfer have become the subjects of interest. with regard to jurisdictional claims in The flow in the intake and exhaust manifolds of an automotive intake and exhaust published maps and institutional affil- system is a typical pulsating flow. The flow and heat transfer characteristics of the intake iations. and exhaust manifolds directly affect the efficiency of the downstream catalyst. Increasingly stringent emission standards require high efficiency of exhaust catalysts. According to Host et al. [1], management of exhaust system heat losses is critical for after-treatment system control and optimization. Therefore, the study of pulsating flows and their heat Copyright: © 2021 by the authors. transfer is a significant problem for optimizing the design of automotive exhaust systems. Licensee MDPI, Basel, Switzerland. Experimental, analytical, and numerical studies on fluid flow and heat transfer of This article is an open access article pulsating flows have been conducted by numerous researchers. The characteristics of distributed under the terms and laminar pulsating flow in a long pipe with constant wall heat flux were experimentally and conditions of the Creative Commons numerically investigated by Zhao and Cheng [2]. The results of the experiment and numer- Attribution (CC BY) license (https:// ical solution, such as the time-resolved fluid temperature and space-cycle averaged Nusselt creativecommons.org/licenses/by/ number, were similar. An experimental study was carried out for laminar pulsating pipe 4.0/).

Energies 2021, 14, 3953. https://doi.org/10.3390/en14133953 https://www.mdpi.com/journal/energies Energies 2021, 14, 3953 2 of 20

flow with constant wall heat flux by Habib [3]. It has been reported that, compared with the Reynolds number, the Nusselt number is strongly affected by the pulsation frequency. However, an analytical method for pulsating laminar convection heat transfer in a pipe was studied by Yu et al. [4]. The results showed that pulsation does not affect the time- averaged Nusselt number. Guo and Sung [5] studied pulsating laminar flows with different amplitudes. It was observed that for small amplitudes, the Nusselt numbers in various forms lead to inconsistent results; however, at higher amplitudes, heat transfer is always enhanced. Theory analysis studied by Hsiao [6] of a steady, two-dimensional, incompress- ible, micropolar, and nanofluid laminar flow reported distributions of the local convective heat transfer coefficient and the temperature of the stretching sheet. Many dimension- less parameters such as the Prandtl number, the Eckert number, the Brownian motion number et al. influence the heat and mass transfer performance of the stretching sheet. For turbulent pulsating flow, the characteristics of convection heat transfer in a pipe with a constant wall temperature were numerically studied by Wang and Zhang [7]. It has been reported that the Womersley number is a critical parameter in the study of pulsating flow and heat transfer. An experimental investigation of pulsating turbulent flow in a pipe with constant heat flux was studied by Elshafei et al. [8]. The results showed that the total Nusselt number was strongly affected by both the Reynolds number and pulsation frequency. The value of the local Nusselt number either increased or decreased over the steady flow value. The heat transfer in an oscillating flow in a cylindrical pipe was experimentally studied by Bouvier et al. [9]. It was observed that the determination of the heat flux by using wall temperatures exclusively or fluid temperatures measured at different radial positions yields different results. In addition to the conditions of different Reynolds numbers and pulsation frequencies, the influence of pulsator location on heat transfer in a pipe with constant heat flux was experimentally investigated by Patel and Attal [10]. The results indicated that the Nusselt number was strongly affected by both the pulsation frequency and Reynolds number when the pulsation mechanism was downstream of the tested pipe exit. The investigation by Wantha [11] also reported that both the pulsation frequency and amplitude of the pulsating flow play important roles in the heat transfer of pulsating flows. Nishandar et al. [12] highlighted that higher values of the local heat transfer coefficient occurred at the entrance of the tested pipe, and the mean heat transfer coefficient increased if pulsation was created in the flow of air. An experimental study of convective heat transfer and pressure drop in a helically coiled tube was investigated by Khosravi-Bizhaem et al. [13]. The findings indicated that the greatest heat transfer intensification occurred at a low Reynolds number, where the pulsating flow could affect the laminar boundary layer significantly compared with the turbulent pulsating flow. From these studies, it can be observed that many factors affect the heat transfer in pulsating flows. However, the main physical mechanisms of these factors’ influence on heat transfer have not been fully described. An experimental investigation by Shiibara et al. [14] applied a technique using infrared thermography to measure the spatio–temporal heat transfer to clarify the mechanism of heat transfer enhancement in a pipe flow upon sudden acceleration and deceleration. An experimental study by Plotnikov and Zhilkin [15] on the thermal and mechanical characteristics of the pulsating flow in the intake system of a turbocharged piston engine reported the influence of external turbulence on the thermal and mechanical characteristics of pulsating flows. Simonetti et al. [16] experimentally investigated the instantaneous characteristics of the flow field and heat transfer in pulsating flows representative of engine exhaust flow operating conditions. A 1D analytical formulation of convective heat transfers in engine exhaust-type turbulent pulsating flows was also presented. The velocity amplitude ratio was identified as representative of the predominant heat transfer enhancement mechanism. Although there have been many studies on heat transfer in pulsating flow, almost all of them are concentrated in straight pipes. Curved pipes as a popular “passive enhancement” technique for heat transfer are widely used in a wide range of industrial applications [17]. Energies 2021, 14, 3953 3 of 20

The steady turbulent flow and heat transfer in the curved pipe was studied by Guo et al. [18]. Under the same geometric shape of the curved pipe, the present study also conducted the experiment of steady flow. Compared with the reference [18], the length of the test section and the temperature measurement points in each cross-section were increased in the present study to get more detailed temperature field information. Many researchers have studied the instantaneous velocity field of pulsating flow in curved pipes [19–22]. The pulsating flow in curved pipes is more complicated than that in straight pipes. Unsteady secondary motions, such as Dean vortices and Lyne vortices, were observed in these studies. Few researchers have investigated the heat transfer characteristics of pulsating flows in curved pipes. The pulsating flow in the tailpipe of a valveless Helmholtz pulse combustor was investigated by Zhai et al. [23]. Based on experimental data, a Nusselt correlation was proposed for the pulsating flow in the straight, 45◦, 90◦, and 135◦ curved tailpipe. Using the same experimental instrument, Xu et al. [24] studied the pulsating flow in the curved tailpipe. This study also included a simulation verification. The flow-reversing, Dean vortex forming, shedding, and reforming processes at the inlet and exit of the curved section contribute to convective heat transfer enhancement. To conclude this review, it should be noted that the measurements of temperature fields inside pipes have rarely been reported owing to the difficulty of measuring the internal temperature of pipes in pulsating flow. In curved pipes, owing to the secondary flow, the internal temperature field inevitably changes after the curvature part, which leads to changes in the local heat transfer characteristics. The catalyst is installed downstream of the exhaust manifold; therefore, the study of the temperature field inside the straight and curved pipes can be used to improve the efficiency of the catalyst. In addition, in the existing studies, the constant wall heat flux thermal boundary condition was used by Zhao and Cheng [2], Habib [3], Yu et al. [4], Guo and Sung [5], Elshafei et al. [8], Patel and Attal [10], and Khosravi-Bizhaem et al. [13]. The constant wall temperature thermal boundary condition was used by Wang and Zhang [7] and Bouvier et al. [9]. Few researchers have studied the heat transfer of pulsating flow in curved pipes based on the third type of wall thermal boundary condition (the heat transfer coefficient of the wall and ambient temperature are defined). Automotive intake and exhaust manifolds are directly exposed to the environment. This situation is more appropriate for this type of wall thermal boundary condition. Therefore, the third type of wall thermal boundary condition was employed to the numerical simulation in this study. Both experiment and simulation have been applied to investigate the turbulent pulsat- ing flow and heat transfer in straight and 90◦ curved pipes, which are often used in engine manifolds. The aim of this study is to clarify the heat transfer performance of pulsating flow in straight and 90◦ curved pipes and analyze the heat transfer mechanism in combination with numerical simulation. The steady turbulent flow was used as a comparison to confirm whether the pulsating flow enhances or suppresses heat transfer. In the experiment, a hot air generator was applied to produce the high-temperature air of the inlet conditions. The pulsating flow was produced by a steady flow, together with a pulsation generator. The velocity and temperature fields were measured by hot-wire anemometers and thermocouples separately. The numerical simulation reported the instan- taneous temperature field and velocity field of the pulsating flow, as well as the effects of sec- ondary flow and flow impingement in the curved pipe on the heat transfer characteristics.

2. Experimental Method 2.1. Experimental Setup The experimental device diagram shown in Figure1 was designed and applied to investigate the influences of the pulsating flow in straight pipe and 90◦ curved pipes on forced-convection heat transfer. Air as an operating fluid is heated by a hot air generator (HAP 3100, Hakko Electric, Tokyo, Japan) in this open-loop system and passed through the pipes to the atmosphere. This experimental system can provide both steady and pulsating flows. As shown in the bottom left of Figure1, the pulsating flow was generated by rotating Energies 2021, 14, 3953 4 of 20

a disk, and four vent holes were arranged at even intervals on the disk. The frequency of the pulsating flow was realized by an AC motor that controlled the rotating speed of the disk. The steady flow was achieved by keeping the disk at a specific position where the hole on the disk was completely opened. The coordinate systems X, Y, and Z represent the streamwise direction, horizontal direction of the cross-section of the pipes, and vertical Energies 2021, 13, x FOR PEER REVIEW 5 of 22 direction of the cross-section of the pipes, respectively.

Figure 1. DiagDiagrammaticrammatic sketch sketch ofof experimental experimental apparatus apparatus and and coordinate coordinate system system..

T34Schematic K-type diagramsthermocouples of the were test used pipes to are measure shown the in Figurehot air 2time. The-averaged pipes were temper- made of aluminum,ature of each and cross the-section. processed As shown inner in and Figure outer 3c, diameters each section of comprised the pipes were36 temperature 32 and 40 mm, respectively.measurement points. According The straight to [18], and there curved are not pipes enough have 12 temperature and 15 temperature measuring measure- points in thement area cross formed-sections, by respectively. secondary flow T32 toK- capturetype thermocouples the detailed were temperature used to measure distribution. the In thehot presentair temperature study, theoscillations number under of measurement pulsating flow. holes was increased to 126. Among these holes, 120 holes with a diameter of 1.6 mm were drilled on the top surface of the pipes for the K-type thermocouple (T34, Okazaki, Kobe, Japan) insertion to measure the air temperature, and six holes with a diameter of 8 mm were drilled for another type of K-type thermocouple (T32, Okazaki, Kobe, Japan) insertion to measure the temperature oscillation under pulsating flow. As shown in Figure3b, the T32 K-type thermocouple is composed of a 13 µm thermocouple and a 25 µm thermocouple. Two holes with a diameter of 5 mm were drilled on the bottom surfaces of the upstream and downstream pipes, respectively. A hot-wire anemometer (0251R-T5, Kanomax, Andover, NJ, USA) was installed in these two holes to measure the inlet and outlet velocities of the hot air after calibration with a pitot tube under the high temperature. Figure3a,b shows the methods used to measure the velocity and temperature, respectively. The temperature field and velocity are measured separately as in Figure3a. The temperature field was measured after the velocity condition had been measured, so the influence of the size of the hot wire on the temperature field measurement of the test part can be ignored. The temperature fields of corresponding cross-sections as shown in Figure2 were measured one by one, and the temperatures of the 36 points in each cross-section as shown in Figure3c were measured point by point. Therefore, the influence of the size of the T34 K-type thermocouple on the measurement results can be ignored. Although the T32 K-type thermocouple as shown in Figure3b is relatively large, it will affect the downstream flow field and temperature distribution. Thus, we measured the temperatures of corresponding cross-sections one by one. When a hole in Figure3b is inserted by the thermocouple, the other holes are filled with screws to reduce Figure 2. Diagrammatic sketch of measurement points on pipes (top view): (a) straight pipe; (b) thecurved measurement pipe; (c) upstream error. pipe; (d) downstream pipe [18].

Energies 2021, 13, x FOR PEER REVIEW 5 of 22

Figure 1. Diagrammatic sketch of experimental apparatus and coordinate system.

T34 K-type thermocouples were used to measure the hot air time-averaged temper- ature of each cross-section. As shown in Figure 3c, each section comprised 36 temperature Energies 2021, 14, 3953 measurement points. The straight and curved pipes have 12 and 15 temperature measure- 5 of 20 ment cross-sections, respectively. T32 K-type thermocouples were used to measure the hot air temperature oscillations under pulsating flow.

Energies 2021, 13, x FOR PEER REVIEWFigureFigure 2. Diagrammatic 2. Diagrammatic sketch of sketch measurement of measurement points on pointspipes (top on pipesview): (top(a) straight view): pipe; (a) straight 6(b of) 22 pipe; curved pipe; (c) upstream pipe; (d) downstream pipe [18]. (b) curved pipe; (c) upstream pipe; (d) downstream pipe [18].

FigureFigure 3. 3. CrossCross-section-section of of pipes pipes (from (from upstream upstream view view):): (a (,ab,)b measurement) measurement methods; methods; (c) ( cmeasure-) measurement mentpoints points [18]. [18].

AsT34 shown K-type in thermocouplesFigure 2, to facilitate were the used subsequent to measure discussion, the hot airthe time-averaged first measurement tempera- sectionture of named each cross-section. “Inlet” at the Asoutlet shown of the in upstream Figure3c, pipe each is sectiondefined comprisedas the origin. 36 S1 temperature to S10 representmeasurement the ten points. measured The cross straight-sections and curvedin the straight pipeshave pipe. 12The and four 15 sections temperature of the measure-90° curvedment cross-sections, part in the curved respectively. pipe were T32 numbered K-type thermocouples as S3-0, S3-30, S3 were-60, usedand S3 to- measure90. The re- the hot mainingair temperature cross-sections oscillations were numbered under pulsating S1, S2, and flow. S4–S10. The outlet of the downstream pipe wasAs shownset as the in “Outlet” Figure2, section. to facilitate the subsequent discussion, the first measurement sectionTo examine named “Inlet”the inflow at theconditions outlet of of thesteady upstream and pulsating pipe is flows defined at the as the“Inlet” origin. section, S1 to S10 asrepresent shown in the Figure ten measured4, the time history cross-sections of the streamwise in the straight velocity pipe. of both The steady four sectionsflow and of the pulsating90◦ curved flow part was in measured the curved using pipe a hot were-wire numbered anemometer. as S3-0, The sampling S3-30, S3-60, frequency and S3-90. was The 10,000remaining Hz, and cross-sections the frequency were of the numbered pulsating S1, flow S2, andwas S4–S10.30 Hz. The The time outlet-averaged of the downstreamveloci- tiespipe ofwas the steady set as theand “Outlet” pulsating section. flows were almost the same. To examine the inflow conditions of steady and pulsating flows at the “Inlet” section, as shown in Figure4, the time history of the streamwise velocity of both steady flow and

Figure 4. Instantaneous velocities at the “Inlet” section of the steady flow and pulsating flow.

Energies 2021, 13, x FOR PEER REVIEW 6 of 22

Figure 3. Cross-section of pipes (from upstream view): (a,b) measurement methods; (c) measure- ment points [18].

As shown in Figure 2, to facilitate the subsequent discussion, the first measurement section named “Inlet” at the outlet of the upstream pipe is defined as the origin. S1 to S10 represent the ten measured cross-sections in the straight pipe. The four sections of the 90° curved part in the curved pipe were numbered as S3-0, S3-30, S3-60, and S3-90. The re- Energies 2021, 14, 3953 maining cross-sections were numbered S1, S2, and S4–S10. The outlet of the downstream6 of 20 pipe was set as the “Outlet” section. To examine the inflow conditions of steady and pulsating flows at the “Inlet” section, as shown in Figure 4, the time history of the streamwise velocity of both steady flow and pulsating flow was measured using a hot-wire anemometer. The sampling frequency was pulsating flow was measured using a hot-wire anemometer. The sampling frequency was 10,00010,000 Hz,Hz, and the frequency of of the the pulsating pulsating flow flow w wasas 30 30 Hz. Hz. The The time time-averaged-averaged veloci- velocities ofties the of steadythe steady and and pulsating pulsating flows flows were were almost almost the the same. same.

FigureFigure 4. InstantaneousInstantaneous velocities velocities at atthe the “Inlet” “Inlet” section section of the of thesteady steady flow flow and andpulsating pulsating flow.flow.

2.2. Data Processing Owing to the insufficient dynamic properties of the temperature sensor and the interpretation of recorded signals, which are composed of static and dynamic temperatures, the fluid temperature in pulsating flow is one of the most difficult and complex flow parameters to be measured [25]. A reliable technique studied by Tagawa et al. [26] for estimating thermocouple time constants without any dynamic calibration was applied in the present study to estimate the real hot air temperature of the pulsating flow. The first-order lag systems of the two thermocouples were used to obtain the fluid temperatures (Tg1 and Tg2) using the following equations:

T = T + τ G  g1 1 1 1 , (1) Tg2 = T2 + τ2G2

where T, τ, and G represents the raw temperature, time constant, and derivative of T, respectively. The subscripts “1” and “2” represent the thermocouples of 13 µm and 25 µm in diameter, respectively. The highest similarity between Tg1 and Tg2 by maximizing the correlation coefficient R is as follows: 0 0 Tg1Tg2 R = q q (2) 0 2 0 2 Tg1 Tg2 Equation (2) was used to diminish the effect of the noise and the irrelevant signal. The time constants to maximize R should satisfy the following condition:

∂R ) ∂τ = 0 1 (3) ∂R = 0 ∂τ2

Simultaneously, the above equations can finally obtain the fluid temperatures (Tg1 and Tg2) after calculating the time constants τ1 and τ2. The time constants of the 13 and 25 µm thermocouples are 9.4 and 21.8 ms, respectively. Energies 2021, 13, x FOR PEER REVIEW 7 of 22

2.2. Data Processing Owing to the insufficient dynamic properties of the temperature sensor and the in- terpretation of recorded signals, which are composed of static and dynamic temperatures, the fluid temperature in pulsating flow is one of the most difficult and complex flow pa- rameters to be measured [25]. A reliable technique studied by Tagawa et al. [26] for esti- mating thermocouple time constants without any dynamic calibration was applied in the present study to estimate the real hot air temperature of the pulsating flow. The first-order lag systems of the two thermocouples were used to obtain the fluid temperatures (Tg1 and Tg2) using the following equations:

= + , (1) = + where T, τ, and G represents the raw temperature, time constant, and derivative of T, respectively. The subscripts “1” and “2” represent the thermocouples of 13 μm and 25 μm in diameter, respectively. The highest similarity between Tg1 and Tg2 by maximizing the correlation coefficient R is as follows: = (2)

Equation (2) was used to diminish the effect of the noise and the irrelevant signal. The time constants to maximize R should satisfy the following condition: = 0⎫ (3) = 0⎬ Energies 2021, 14, 3953 ⎭ 7 of 20

Simultaneously, the above equations can finally obtain the fluid temperatures (Tg1 and Tg2) after calculating the time constants τ1 and τ2. The time constants of the 13 and 25 μm thermocouplesFigure5 shows are a 9.4 sample and 21.8 of the ms, comparisonrespectively. of the original temperature measured by theFigure 13 and 5 shows 25 µm a thermocouplessample of the comparison and the estimation of the original of these temperature two thermocouples. measured by The the 13 and 25 μm thermocouples and the estimation of these two thermocouples. The measurement position in this sample was at the midpoint of the upstream pipe. The measurement position in this sample was at the midpoint of the upstream pipe. The esti- estimated temperatures of these two thermocouples overlapped well, and the amplitudes mated temperatures of these two thermocouples overlapped well, and the amplitudes of of these two estimated temperatures were higher than the measured values. these two estimated temperatures were higher than the measured values.

Figure 5. A sample of the comparison of the original and estimated temperatures.

To calculate the total and local heat transfer in the pipes, the thermophysical properties of hot air to calculate heat transfer were obtained at the mean temperature as follows:

T + T T = i o (4) m 2 where the subscripts “i” and “o” denote the “Inlet” and “Outlet” sections, respectively. In both the steady flow and the pulsating flow, the spatial average temperature of the Nc = 36 points in the cross-section, as shown in Figure3c, was used in the calculation. The temperature of each point was the time average of Tmea = 30 s. The local heat flow rate (Qx) was calculated using the following equation: . Qx = mCp(Tx−∆x − Tx+∆x) (5) . where Cp is the constant pressure specific, m is the mass flow rate expressed as follows: . m = ρAcU (6)

where ρ denotes the density of air, Ac denotes the cross-sectional area of the square pipes, and U denotes the time average of the velocity. ∆x is half the distance between two adjacent cross-sections in the streamwise direction. Tx is the local position temperature, expressed as follows: n=N ! 1 Z Tmea 1 c Tx = ∑ Tnx(t) dt (7) Tmea 0 Nc n=1

where Tnx is the temperature of the nth point in the local cross-section, t is the temperature sampling time. Finally, the local heat flux (qx) was obtained as follows:

Qx qx = (8) Aw Energies 2021, 14, 3953 8 of 20

where Aw denotes the pipe wall area of the local section at x. Four rectangular pipe walls are used for the straight pipe. The curved part of the curved pipe is composed of two sectors and two curved surfaces. Because the total wall areas of the test sections in the straight and curved pipes are different, it is appropriate to use the total heat flux to characterize the heat transfer performance. The total heat flux (qt) was calculated using the following equation:

Qt qt = (9) Atw

where Atw denotes the total wall area of the test section, and Qt denotes the total heat flow rate, expressed as follows: . Qt = mCp(Ti − To) (10) The measurement accuracies of the major parameters used are shown in Table1.

Table 1. Major parameter uncertainties [18].

Parameter Uncertainty Parameter Uncertainty Pipe diameter 0.08 mm (0.25%) Velocity 1.2 m/s Energies 2021, 13, x FOR PEER REVIEW Pipe length 1.5 mm (0.08%) Air temperature 0.2 K9 of 22

Curvature 0.1 mm (0.17%)

3.3. NumericalNumerical S Simulationsimulations NumericalNumerical simulations simulations were were implemented implemented using using CONVERGECONVERGETM (Convergent(Convergent Sci- Science, Madison,ence, Madison WI, USA)., WI, U.S. The). CHTThe CHT method method was was used used to solve to solve the flowthe flow and and heat heat transfer transfer in both thein both solid the and solid fluid and regions. fluid regions. The computationalThe computational domain domain included included an an upstream upstream pipe, pipe, the mainthe main test sectiontest section (curved (curved pipe/straight pipe/straight pipe), pipe), and and a downstreama downstream pipe pipe that that was was the the same assame the as piping the piping layout layout in the in experiment.the experiment. A A modified modified cut-cell cut-cell CartesianCartesian mesh genera- generation methodtion method was was used u forsed thefor geometricthe geometric surface. surface. The The computational computational domain domain waswas discretizeddiscre- usingtized using cube meshes,cube meshes, and theand mesh the mesh size wassize was 1 mm. 1 mm. Figure Figure6 shows 6 shows the detailsthe details of theof the mesh. mesh.

FigureFigure 6.6. Computational mesh mesh in in the the curved curved pipe. pipe. (a) (sidea) side view, view, (b) (upstreamb) upstream view view at the at cross the- cross- sectionsection [[18]18]..

InIn thethe CHT simulation, simulation, the the temperature temperature and and heat heat flux flux of the of thefluid fluid and and solid solid regions regions werewere consistentconsistent atat thethe interface.interface. The interface boundary boundary definition definition is is the the connecting connecting sur- surface betweenface between the fluidthe fluid and and solid solid regions. regions. For For the the turbulence turbulence model, model, the the RNG RNG k–k–εε modelmodel was appliedwas applied to calculate to calculate the the turbulent turbulent flows. flows. In In addition, addition, the the law law ofof thethe wall was adopted adopted for thefor velocitythe velocity calculation calculation on theon the solid solid walls walls to dealto deal with with the the boundary boundary layer layer on on the the wall wall using theusing RNG the k– RNGε model. k–ε model. For the For temperature the temperature law of law the of wall the boundarywall boundary condition, condition, the Han the and ReitzHan and model Reitz [27 model] was [27] used was to used account to account for compressible for compressible effects effects in a pulsatingin a pulsating flow. flow. In this study, the Reynolds number is expressed as follows: = (11) where D denotes the hydraulic diameter of the pipe, which is the same as the inner diam- eter of the pipe, and ν denotes the kinematic viscosity of the fluid. The Dean number was first proposed by Dean (1959) to characterize curved pipe flows, and it was defined using the following equation:

= (12) 2

where Rc denotes the radius of curvature of the curved pipe. The most commonly used dimensionless parameter to characterize pulsating flow is the Womersley number, which is given by: = (13) 2 where ω is the angular frequency of the pulsation. The simulation inlet boundary conditions for the velocity and temperature were measured by the hot-wire and the thermocouple separately in the experiment. The outlet

Energies 2021, 14, 3953 9 of 20

In this study, the Reynolds number is expressed as follows:

UD Re = (11) ν where D denotes the hydraulic diameter of the pipe, which is the same as the inner diameter of the pipe, and ν denotes the kinematic viscosity of the fluid. The Dean number was first proposed by Dean (1959) to characterize curved pipe flows, and it was defined using the following equation: s D De = Re (12) 2Rc

where Rc denotes the radius of curvature of the curved pipe. The most commonly used dimensionless parameter to characterize pulsating flow is the Womersley number, which is given by:

D r ω α = (13) 2 ν

where ω is the angular frequency of the pulsation. The simulation inlet boundary conditions for the velocity and temperature were measured by the hot-wire and the thermocouple separately in the experiment. The outlet pressure boundary condition was set as 101.325 kPa, and the temperature of the reverse flow at the outlet was set at 300 K. A no-slip wall boundary condition was employed on the solid domain side of the interface. The convection boundary condition was adopted on the outer side of the solid domain. The ambient temperature outside the pipe was set as 298.15 K, which is the same as the room temperature in the experiment. The heat transfer coefficient of this convection boundary was selected to be 14 W/m2·K. The heat transfer coefficient of 14 W/m2·K was chosen because previous studies [18] confirmed that the simulation results were in good agreement with the experimental results. For the experimental and numerical conditions, the inlet temperature was set to 402 K. The time-averaged Reynolds number was approximately 60,000 in both the straight and the curved pipes. The Dean number was 31,000 in the curved pipe. The Womersley number was 43.1, in the pulsating flows.

4. Results and Discussion 4.1. Reverse Flow at the Outlet under Pulsating Flow Conditions Many experimental and numerical studies have shown that reverse flow occurs under pulsating flow conditions, particularly in the large amplitude of the pulsating flow [28–30]. As shown in Figure7, the time history of the streamwise velocity of the pulsating flow at the “Outlet” was measured using a hot-wire anemometer. The signal output of the hot-wire anemometer was a voltage signal, and the velocity value was calculated from the voltage signal through a linear relationship. The green circles in the figure indicate that, during the deceleration of the pulsating flow, the voltage signal changes abruptly. The voltage is a scalar quantity, and the velocity is a vector quantity, thus the velocity flows in the opposite direction during these regions. Energies 2021, 13, x FOR PEER REVIEW 10 of 22

pressure boundary condition was set as 101.325 kPa, and the temperature of the reverse flow at the outlet was set at 300 K. A no-slip wall boundary condition was employed on the solid domain side of the interface. The convection boundary condition was adopted on the outer side of the solid domain. The ambient temperature outside the pipe was set as 298.15 K, which is the same as the room temperature in the experiment. The heat trans- fer coefficient of this convection boundary was selected to be 14 W/m2·K. The heat transfer coefficient of 14 W/m2·K was chosen because previous studies [18] confirmed that the sim- ulation results were in good agreement with the experimental results. For the experi- mental and numerical conditions, the inlet temperature was set to 402 K. The time-aver- aged Reynolds number was approximately 60,000 in both the straight and the curved pipes. The Dean number was 31,000 in the curved pipe. The Womersley number was 43.1, in the pulsating flows.

4. Results and Discussion 4.1. Reverse Flow at the Outlet under Pulsating Flow Conditions Many experimental and numerical studies have shown that reverse flow occurs un- der pulsating flow conditions, particularly in the large amplitude of the pulsating flow [28–30]. As shown in Figure 7, the time history of the streamwise velocity of the pulsating flow at the “Outlet” was measured using a hot-wire anemometer. The signal output of the hot-wire anemometer was a voltage signal, and the velocity value was calculated from the voltage signal through a linear relationship. The green circles in the figure indicate that, during the deceleration of the pulsating flow, the voltage signal changes abruptly. The Energies 2021, 14, 3953 10 of 20 voltage is a scalar quantity, and the velocity is a vector quantity, thus the velocity flows in the opposite direction during these regions.

FigureFigure 7. 7.The The voltage voltage signal signal and and the the velocity velocity of theof the pulsating pulsating flow flow at the at “Outlet”the “Outlet” section. section.

TheThe velocity velocity experiment experiment results results at theat the “Outlet” “Outlet” verify verify the the existence existence of reverse of reverse flow flow underunder the the condition condition of of pulsating pulsating flow. flow. The The reverse reverse flow flow inhaled inhaled the dischargedthe discharged air into air into thethe pipe, pipe, and and the the temperature temperature of theof the air air was was low. low. Therefore, Therefore, the the reverse reverse flow flow phenomenon phenomenon causedcaused the the heat heat transfer transfer performance performance at theat the outlet outlet section section to be to differentbe different from from that that at the at the upstream section. The specific effect of reverse flow on heat transfer is discussed in detail upstream section. The specific effect of reverse flow on heat transfer is discussed in detail later section. later section. 4.2. Circumferential Temperature Fields in the Cross-Sections For the convenience of description, the steady flow in the straight pipe, the pulsating flow in the straight pipe, the steady flow in the curved pipe, and the pulsating flow in the curved pipe were referred to as “SS”, “PS”, “SC”, and “PC”, respectively. For the circumferential time-averaged temperature fields, color contours of temperature for the

experiment were created using MATLAB (MathWorks Inc., Portola Valley, CA, USA) codes based on 36 temperature measured points of each cross-section. The inlet temperature fields of the steady and pulsating flows in the straight and curved pipes are shown in Figure8. At the “Inlet” section, the temperature field is almost the same under these four experimental conditions. The temperature contours show a nearly concentric circular distribution. In the same pulsation generator device, the stereo particle image velocimetry (PIV) measurement in a double 90◦ square pipe was studied by Oki [22]. It was reported that because of the rotating disk effect, the velocity distribution 3D upstream of the first curved entrance was point-symmetrical, and the distribution shape was consistent with the temperature distribution shape in the present study. Figures9 and 10 show the temperature contours of different cross-sections of the “SS” and “PS”, respectively. In the temperature contours from S1 to S10, the temperature gradually decreased. Compared to the “SS”, the temperature drop of the “PS” was less. The temperature in each cross-section decreased from the center to the surroundings. Comparing the central areas of the cross-sections of the “SS” and “PS”, the temperature distribution in the high-temperature core area of the “SS” was concentrated, while that of “PS” was larger. Energies 2021, 13, x FOR PEER REVIEW 11 of 22

4.2. Circumferential Temperature Fields in the Cross-Sections For the convenience of description, the steady flow in the straight pipe, the pulsating flow in the straight pipe, the steady flow in the curved pipe, and the pulsating flow in the curved pipe were referred to as “SS”, “PS”, “SC”, and “PC”, respectively. For the circum- ferential time-averaged temperature fields, color contours of temperature for the experi- ment were created using MATLAB (MathWorks Inc., Portola Valley, CA, USA) codes based on 36 temperature measured points of each cross-section. The inlet temperature fields of the steady and pulsating flows in the straight and curved pipes are shown in Energies 2021, 13, x FOR PEER REVIEWFigure 8. At the “Inlet” section, the temperature field is almost the same under11 of these22 four

experimental conditions. The temperature contours show a nearly concentric circular dis- tribution. In the same pulsation generator device, the stereo particle image velocimetry 4.2.(PIV) Circumferential measurement Temperature in a double Fields 90° in squarethe Cross pipe-Sections was studied by Oki [22]. It was reported that Forbecause the convenience of the rotating of description, disk effect, the steadythe velocity flow in distribution the straight pipe, 3D upstream the pulsating of the first flowcurved in the entrance straight was pipe, point the steady-symmetrical, flow in the and curved the pipe,distribution and the pulsatingshape was flow consistent in the with curvedthe temperature pipe were referreddistribution to as “SS”shape, “PS” in the, “SC” present, and “PC” study., respectively. For the circum- ferential time-averaged temperature fields, color contours of temperature for the experi- ment were created using MATLAB (MathWorks Inc., Portola Valley, CA, USA) codes based on 36 temperature measured points of each cross-section. The inlet temperature fields of the steady and pulsating flows in the straight and curved pipes are shown in Figure 8. At the “Inlet” section, the temperature field is almost the same under these four experimental conditions. The temperature contours show a nearly concentric circular dis- tribution. In the same pulsation generator device, the stereo particle image velocimetry (PIV) measurement in a double 90° square pipe was studied by Oki [22]. It was reported Energies 2021, 14, 3953 that because of the rotating disk effect, the velocity distribution 3D upstream of the first 11 of 20 curved entrance was point-symmetrical, and the distribution shape was consistent with the temperature distribution shape in the present study.

Figure 8. Temperature contour comparison among the “Inlet” conditions: (a) ”SS”; (b) “PS”; (c) “SC”; (d) ”PC”.

Figures 9 and 10 show the temperature contours of different cross-sections of the “SS” and “PS”, respectively. In the temperature contours from S1 to S10, the temperature grad- ually decreased. Compared to the “SS”, the temperature drop of the “PS” was less. The temperature in each cross-section decreased from the center to the surroundings. Com- paring the central areas of the cross-sections of the “SS” and “PS”, the temperature distri- bution in the high-temperature core area of the “SS” was concentrated, while that of “PS” FigureFigure 8. 8.Temperature contour comparison among the “Inlet” conditions: (a) a ”SS”; (b) b “PS”; (c) c was larger.Temperature contour comparison among the “Inlet” conditions: ( ) ”SS”; ( ) “PS”; ( ) “SC”; “SC”;(d) ”PC”.(d) ”PC”.

Figures 9 and 10 show the temperature contours of different cross-sections of the “SS” and “PS”, respectively. In the temperature contours from S1 to S10, the temperature grad- ually decreased. Compared to the “SS”, the temperature drop of the “PS” was less. The temperature in each cross-section decreased from the center to the surroundings. Com- paring the central areas of the cross-sections of the “SS” and “PS”, the temperature distri- bution in the high-temperature core area of the “SS” was concentrated, while that of “PS” was larger.

Energies 2021, 13, x FOR PEER REVIEW 12 of 22

Figure 9. Temperature contours of different cross-sections of the “SS”. Figure 9. Temperature contours of different cross-sections of the “SS”.

FigureFigure 10. 10. TemperatureTemperature contours contours of of different different cross cross-sections-sections ofof thethe “PS”.“PS”.

TheThe temperature temperature contours contours of of the the different different cross cross-sections-sections ofof “SC”“SC”and and “PC” “PC” are are shown shown inin Figures Figures 11 11 and and 12, 12 respectively., respectively. When When compared compared to the temperaturetemperature fields fields in in the the straight straight pipe,pipe, the the temperature fields fields in in the the curved curved part andpart downstream and downstream of the curved of the part curved changed part changedsignificantly. significantly. Owing to Owi theng influence to the influence of the centrifugal of the centrifugal force at the force curved at partthe curved (from S2-0 part to S3), the high-temperature core gradually shifted to the outer side. In a curved pipe, the (from S2-0 to S3), the high-temperature core gradually shifted to the outer side. In a curved typical secondary flow structure is the Dean vortices (two symmetrical counter-rotating pipe, the typical secondary flow structure is the Dean vortices (two symmetrical counter- vortices). With the generation of the secondary flow, the temperature fields gradually rotating vortices). With the generation of the secondary flow, the temperature fields grad- formed a vortex secondary distribution. In downstream of the curved part, this secondary uallyflow formed distribution a vortex gradually secondary weakens distribution. along the In flow downstream direction. of The the temperature curved part, fields this sec- of ondary“SC” and flow “PC” distribution showed the gradually same changing weakens trend. along the flow direction. The temperature fields of “SC” and “PC” showed the same changing trend. The temperature near the inner side is particularly low in the S90, which is the exit of the curved part. Combined with previous study [23], this phenomenon was caused by the separation of air and the pipe wall.

Figure 11. Temperature contours of different cross-sections of the “SC”.

Energies 2021, 13, x FOR PEER REVIEW 12 of 22

Figure 9. Temperature contours of different cross-sections of the “SS”.

Figure 10. Temperature contours of different cross-sections of the “PS”.

The temperature contours of the different cross-sections of “SC” and “PC” are shown in Figures 11 and 12, respectively. When compared to the temperature fields in the straight pipe, the temperature fields in the curved part and downstream of the curved part changed significantly. Owing to the influence of the centrifugal force at the curved part (from S2-0 to S3), the high-temperature core gradually shifted to the outer side. In a curved pipe, the typical secondary flow structure is the Dean vortices (two symmetrical counter- rotating vortices). With the generation of the secondary flow, the temperature fields grad- ually formed a vortex secondary distribution. In downstream of the curved part, this sec- ondary flow distribution gradually weakens along the flow direction. The temperature fields of “SC” and “PC” showed the same changing trend. Energies 2021, 14, 3953 The temperature near the inner side is particularly low in the S90, which is the12 exit of 20 of the curved part. Combined with previous study [23], this phenomenon was caused by the separation of air and the pipe wall.

Energies 2021, 13, x FOR PEER REVIEW 13 of 22

FigureFigure 11. 11. TemperatureTemperature contours contours of of different different cross cross-sections-sections ofof thethe “SC”.“SC”.

FigureFigure 12. 12. TemperatureTemperature contours contours of of different different cross-sectionscross-sections ofof thethe “SC”. “SC”.

FigureThe temperature 13 shows the near temperature the inner side fields is particularly of the “Outlet” low in of the the S90, “SS” which, “PS is”, the “SC exit”, and of “PC”the curved. As shown part. in Combined Figure 8, withthe “Inlet” previous conditions study [23 of], thisthe “SS phenomenon”, “PS”, “SC was”, and caused “PC” by were the setseparation to be nearly of air the and same. the pipe The wall. “Outlet” temperature distribution can directly show the total temperatureFigure 13 shows difference the temperature between “Inlet” fields of and the “Outlet” “Outlet” ofunder the “SS”,these “PS”, four “SC”,conditions. and “PC”. As shown in Figure8, the “Inlet” conditions of the “SS”, “PS”, “SC”, and “PC” were Regardless of the straight pipe or curved pipe, the “Outlet” temperature of the steady flow set to be nearly the same. The “Outlet” temperature distribution can directly show the condition is higher than that of the pulsating flow. However, comparing Figures 9-12, the total temperature difference between “Inlet” and “Outlet” under these four conditions. temperature reduction of the steady flow was larger than that of the pulsating flow. Re- Regardless of the straight pipe or curved pipe, the “Outlet” temperature of the steady flow gardingcondition the issmall higher temperature than that ofreduction the pulsating of the flow.pulsating However, flow, comparingthe “Outlet” Figures temperature9–12, wasthe lower temperature; it was caused reduction by ofthe the reverse steady flow. flow Reverse was larger flow than is the that process of the pulsatingof returning flow. the airRegarding that has been the small exhausted temperature from the reduction pipe back of the into pulsating the pipe. flow, The the exhausted “Outlet” air temperature was mixed withwas the lower; low it-temperature was caused byambient the reverse air so flow. that Reversethe time flowaverage is the temperature process of returning of the pulsat- the ingair flow that hasat the been “Outlet” exhausted was from lower the than pipe that back of into the thesteady pipe. flow The. exhausted air was mixed with the low-temperature ambient air so that the time average temperature of the pulsating flow at the “Outlet” was lower than that of the steady flow.

Figure 13. Temperature contour comparison among the “Outlet” conditions: (a) “SS”; (b) “PS”; (c) “SC”; (d) “PC”.

4.3. Streamwise Temperature Variation As shown in Figure 14, the average temperature of the cross-sections of the “SS”, “PS”, “SC”, and “PC” decreased as the air flows downstream. The abscissa “X/D” is the streamwise dimensionless length, where D denotes the inner diameter of the pipe. The

Energies 2021, 13, x FOR PEER REVIEW 13 of 22

Figure 12. Temperature contours of different cross-sections of the “SC”.

Figure 13 shows the temperature fields of the “Outlet” of the “SS”, “PS”, “SC”, and “PC”. As shown in Figure 8, the “Inlet” conditions of the “SS”, “PS”, “SC”, and “PC” were set to be nearly the same. The “Outlet” temperature distribution can directly show the total temperature difference between “Inlet” and “Outlet” under these four conditions. Regardless of the straight pipe or curved pipe, the “Outlet” temperature of the steady flow condition is higher than that of the pulsating flow. However, comparing Figures 9-12, the temperature reduction of the steady flow was larger than that of the pulsating flow. Re- garding the small temperature reduction of the pulsating flow, the “Outlet” temperature was lower; it was caused by the reverse flow. Reverse flow is the process of returning the Energies 2021, 14, 3953 air that has been exhausted from the pipe back into the pipe. The exhausted air was mixed 13 of 20 with the low-temperature ambient air so that the time average temperature of the pulsat- ing flow at the “Outlet” was lower than that of the steady flow.

FigureFigure 13. Temperature 13. Temperature contour contour comparison comparison among amongthe “Outlet” the “Outlet”conditions: conditions: (a) “SS”; (b ()a “PS”;) “SS”; (c) ( b) “PS”; “SC”;(c) ( “SC”;d) “PC”. (d) “PC”.

4.3.4.3. Streamwise Streamwise Temperature Temperature Variation Variation As Asshown shown in Figure in Figure 14, the14 ,average the average temperature temperature of the ofcross the-sections cross-sections of the “SS of”, the “SS”, Energies 2021, 13, x FOR PEER REVIEW 14 of 22 “PS“PS”,”, “SC “SC”,”, and and “PC “PC”” decreased decreased as the as air the flows air flows downstream. downstream. The abscissa The abscissa “X/D” “X/D”is the is the streamwisestreamwise dimensionless dimensionless length, length, where where D denotes D denotes the inner the diameter inner diameter of the pipe. of the The pipe. The origin of X/D is defined at the “Inlet”. Figure 14a shows the temperature variation from theorigin “Inlet” of toX/D the is “Outlet”.defined at In the the “Inlet” cases. ofFigure pulsating 14a shows flow (“PS”the temperature and “PC”), variation the temperature from the “Inlet” to the “Outlet”. In the cases of pulsating flow (“PS” and “PC”), the temperature dropped sharply at the “Outlet” because of the influence of the reverse flow. Figure 14b showsdropped the temperaturesharply at the variation “Outlet” along because the of streamwise the influence direction of the reverse from “Inlet” flow. toFigure “S10” 14b after shows the temperature variation along the streamwise direction from “Inlet” to “S10” af- ignoring the effect of reverse flow at the “Outlet”. In the “SS”, the temperature decreased ter ignoring the effect of reverse flow at the “Outlet”. In the “SS”, the temperature de- linearly and monotonously along the streamwise direction. In the “PS”, although the creased linearly and monotonously along the streamwise direction. In the “PS”, although temperature showed a decreasing trend, the decline gradually slowed down during the the temperature showed a decreasing trend, the decline gradually slowed down during “Inlet” to “S10”. From “S10” to the “Outlet”, the temperature decreased sharply. In the two the “Inlet” to “S10”. From “S10” to the “Outlet”, the temperature decreased sharply. In casesthe oftwo the cases curved of the pipe curved (“SC” pipe and (“SC” “PC”), and the “PC”), streamwise the streamwise temperature temperature variation variation was more complicatedwas more compli than thatcated of than the straightthat of the pipe. straight Regardless pipe. Regardless of the steady of the flow steady or pulsatingflow or pul- flow, thesating temperature flow, the exhibitedtemperature a sharp exhibited drop a insharp the curveddrop in part.the curved Then, part. the temperatureThen, the temper- decline slowedature decline until S10. slowed until S10.

FigureFigure 14. Average 14. Average temperatures temperatures in thein the streamwise streamwise direction direction ofof thethe “SS”, “PS”, “PS”, “SC”, “SC”, and and “PC” “PC”:: (a) all (a) measurement all measurement sections, (b) from “Inlet” to S10. sections, (b) from “Inlet” to S10. Among these four conditions, regardless of the “Outlet” section, the temperature re- duction of the pulsating flow condition is smaller than that of the steady flow. In the case of steady flow, from the “Inlet” to the “Outlet”, the temperature changed smoothly and there was no sudden change from “S10” to the “Outlet”. In the cases of pulsating flow, the temperature dropped sharply at the “Outlet” owing to the effect of the reverse flow.

4.4. Temperature Oscillations in Pulsating Flow Some studies [5,11,16] have shown that the velocity amplitude of the pulsating flow is a significant factor that affects the heat transfer performance. However, there are a few studies on the investigation of the local temperature amplitude of the pulsating flow. As shown in Figure 2, there are six temperature measurement points (X/D = 3, 9, 13, 19, 24, and 29) along the streamwise direction in the straight pipe. These points were used to insert a T32 K-type thermocouple to measure the center temperature of each cross-section. Figure 15 shows the time history of the air temperature difference from the time average temperature of the different cross-sections of the “PS”. For convenience of comparison, the time average temperature of each cross-section was set to “zero” for all these condi- tions. The temperature oscillations gradually weakened along the streamwise direction. The closer it is to the pulsation generator, the greater is the amplitude of the temperature. It can be observed from Figure 14 that the greater the amplitude of the temperature, the larger is the temperature decline.

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Among these four conditions, regardless of the “Outlet” section, the temperature reduction of the pulsating flow condition is smaller than that of the steady flow. In the case of steady flow, from the “Inlet” to the “Outlet”, the temperature changed smoothly and there was no sudden change from “S10” to the “Outlet”. In the cases of pulsating flow, the temperature dropped sharply at the “Outlet” owing to the effect of the reverse flow.

4.4. Temperature Oscillations in Pulsating Flow Some studies [5,11,16] have shown that the velocity amplitude of the pulsating flow is a significant factor that affects the heat transfer performance. However, there are a few studies on the investigation of the local temperature amplitude of the pulsating flow. As shown in Figure2, there are six temperature measurement points (X/D = 3, 9, 13, 19, 24, and 29) along the streamwise direction in the straight pipe. These points were used to insert a T32 K-type thermocouple to measure the center temperature of each cross-section. Figure 15 shows the time history of the air temperature difference from the time average temperature of the different cross-sections of the “PS”. For convenience of comparison, the time average temperature of each cross-section was set to “zero” for all these conditions. The temperature oscillations gradually weakened along the streamwise direction. The closer it is to the pulsation generator, the greater is the amplitude of the temperature. It can Energies 2021, 13, x FOR PEER REVIEW 15 of 22 be observed from Figure 14 that the greater the amplitude of the temperature, the larger is the temperature decline.

FigureFigure 15. 15. TemperatureTemperature difference from from the the time time average average temperature temperature of the of thedifferent different cross cross-sections-sections ofof the the “PS”. “PS”.

WhenWhen thethe velocity amplitude amplitude is is constant, constant, the the local local heat heat transfer transfer performance performance depends depends onon the the amplitudeamplitude of the temperature. temperature. A A large large temperature temperature amplitude amplitude can can enhance enhance the heat the heat transfer.transfer.

4.5.4.5. HeatHeat TransferTransfer PerformancePerformance A Analysisnalysis HeatHeat fluxflux isis anan important parameter parameter that that can can reflect reflect heat heat transfer transfer performance. performance. As As shownshown in in FigureFigure 1616,, the the local local heat heat flux flux at at different different positions positions along along the thestreamwise streamwise direction direction intuitively illustrated the heat transfer performance of the “SS”, “PS”, “SC”, and “PC”. intuitively illustrated the heat transfer performance of the “SS”, “PS”, “SC”, and “PC”. The heat flux of the “SS” maintained almost the same value at different positions. At The heat flux of the “SS” maintained almost the same value at different positions. At downstream of the straight pipe, the heat flux slightly decreased. The reason for the de- downstream of the straight pipe, the heat flux slightly decreased. The reason for the crease in heat flux is that in this region, the temperature of the air inside the pipe decreases decrease in heat flux is that in this region, the temperature of the air inside the pipe and the temperature of the pipe wall also decreases, resulting in a smaller temperature decreasesdifference andbetween the temperaturethe pipe wall ofand the ambient pipe wall temperatures. also decreases, According resulting to the inthermal a smaller boundary condition of the pipe wall in this study, the smaller the temperature difference between the pipe wall and ambient temperatures, the smaller the heat flux is. The heat flux change trend of the “PS” was quite different from that of the “SS”. The heat flux of “PS” decreased monotonously along the streamwise direction, except at X/D = 25. Under the pulsating flow of the straight pipe, the local heat flux at the entrance of the test section (X/D = 1–3) was higher than that of the straight pipe. In the subsequent sections (X/D = 3–19), the heat flux of the steady flow increased, and the heat flux differ- ence between the steady flow and pulsating flow gradually increased. The heat flux of X/D = 25 increased sharply; however, this does not indicate that the heat transfer was en- hanced. As discussed in Section 3.1, there was reverse flow, which made the temperature at the “Outlet” abnormally low. In the “SC” and “PC”, owing to the impact of the secondary flow and the high-tem- perature core impingement, the heat flux was maintained at a high level near the outlet of the curved part (X/D = 6–10). At downstream of the curved part (X/D = 10–22), the magni- tude of the heat flux was restored to the same level as that of the straight pipe. Similarly, the heat flux of X/D = 25 increased under the pulsating flow condition of the curved pipe because of the reverse flow; however, this does not indicate the enhancement of heat trans- fer at the location.

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temperature difference between the pipe wall and ambient temperatures. According to Energies 2021, 13, x FOR PEER REVIEW 16 of 22 the thermal boundary condition of the pipe wall in this study, the smaller the temperature difference between the pipe wall and ambient temperatures, the smaller the heat flux is.

FigureFigure 16. 16. HeatHeat flux flux of of the the different different cross cross-sections-sections of the of the“SS”, “SS”, “PS”, “PS”, “SC”, “SC”, and “PC”. and “PC”.

IfThe the heateffectflux of reverse change flow trend was ofignored, the “PS” the wastotal quiteheat flux different from the from “Inlet” that to of “S10” the “SS”. ofThe the heat steady flux flow of “PS”and the decreased pulsating monotonously flow in the curved along pipe the were streamwise 8% and 65% direction, higher than except at thatX/D of = the 25. straight Under thepipe, pulsating respectively. flow The of the heat straight flux of pipe,the steady the local flow heat in the flux straight at the and entrance curved pipes was 64% and 10% higher than that of the pulsating flow, respectively. It is of the test section (X/D = 1–3) was higher than that of the straight pipe. In the subsequent worth noting that at the entrance of the test section, the local heat flux of the pulsating sections (X/D = 3–19), the heat flux of the steady flow increased, and the heat flux difference flow is higher than that of the steady flow, and the closer to the pulsation generator, the between the steady flow and pulsating flow gradually increased. The heat flux of X/D = 25 larger the temperature amplitude is and the higher the local heat flux of the pulsating flow increased sharply; however, this does not indicate that the heat transfer was enhanced. is. As discussed in Section 4.1, there was reverse flow, which made the temperature at the “Outlet”4.6. Numerical abnormally Analysis low.of Heat Transfer Mechanism In the “SC” and “PC”, owing to the impact of the secondary flow and the high- To further study the heat transfer mechanism of the pulsating flow, a CHT simulation temperature core impingement, the heat flux was maintained at a high level near the outlet was used to show more details. of theAt curvedthe beginning part (X/D of the = numerical 6–10). At analysis, downstream both the of theflow curved velocity part and (X/D fluid =temper- 10–22), the aturemagnitude were validated of the heat using flux the wassimulation restored model tothe and same simulation level setup. as that In of previous the straight stud- pipe. iesSimilarly, [18], validation the heat under flux ofsteady X/D flow = 25 conditions increased was under verified. the pulsating The valid flowation conditionof the tem- of the peraturecurved pipeoscillation because in the of the pulsating reverse flow flow; is also however, provided this in does this notstudy. indicate Figure the 17 enhancementshows a comparisonof heat transfer of the at temperature the location. difference from the time-averaged temperature at two dif- ferentIf locations the effect (X/D of reverse = 3, 29) flow in the was experiment ignored, theand totalsimulati heaton. flux For from convenience the “Inlet” of tocom- “S10” of parison,the steady the flowtime andaverage the temperature pulsating flow was in set the to curved“0” for all pipe these were conditions. 8% and 65%Whether higher at than thethat “Inlet” of the (X/D straight = 3) pipe,or “Outlet” respectively. (X/D = 29 The) of heat the fluxtest section, of the steady the amplitude flow in theof the straight tem- and peraturecurved pipesoscillations was 64% can be and well 10%-matched. higher The than max thatimum of the and pulsating minimum flow, temperatures respectively. ap- It is pearworth simultaneously. noting that at Because the entrance the frequency of the test derived section, from the localthe simulation heat flux ofresults the pulsating is much flow loweris higher than than the experimental that of the steady sampling flow, frequency, and the closerthere is to a theslight pulsation deviation generator, in the temper- the larger aturethe temperature between the amplitudeexperiment is and and the the simulation higher the at local some heat instants. flux ofFor the the pulsating validation flow of is. the velocity fields, Oki et al. [31] investigated the velocity fields in the curved pipe by PIV measurement.4.6. Numerical The Analysis numerical of Heat simulation Transfer results Mechanism proposed by Oki et al. were used to com- pare withTo further the PIV study results the of heat the transfer streamwise mechanism velocity ofdistribution the pulsating at the flow, exit a of CHT thesimulation pipe curvedwas used part, to and show they more are in details. good agreement. The simulation in this study is based on the same Atnumerical the beginning method as of Oki the et numerical al., so it is analysis,reliable toboth be used. the flow velocity and fluid tem- perature were validated using the simulation model and simulation setup. In previous studies [18], validation under steady flow conditions was verified. The validation of the

Energies 2021, 14, 3953 16 of 20

temperature oscillation in the pulsating flow is also provided in this study. Figure 17 shows a comparison of the temperature difference from the time-averaged temperature at two different locations (X/D = 3, 29) in the experiment and simulation. For convenience of comparison, the time average temperature was set to “0” for all these conditions. Whether at the “Inlet” (X/D = 3) or “Outlet” (X/D = 29) of the test section, the amplitude of the temperature oscillations can be well-matched. The maximum and minimum temperatures appear simultaneously. Because the frequency derived from the simulation results is much lower than the experimental sampling frequency, there is a slight deviation in the tem- perature between the experiment and the simulation at some instants. For the validation of the velocity fields, Oki et al. [31] investigated the velocity fields in the curved pipe by PIV measurement. The numerical simulation results proposed by Oki et al. were used to compare with the PIV results of the streamwise velocity distribution at the exit of the pipe Energies 2021, 13, x FOR PEER REVIEW 17 of 22 curved part, and they are in good agreement. The simulation in this study is based on the same numerical method as Oki et al., so it is reliable to be used.

FigureFigure 17.17. TheThe experimental experimental and and numerical numerical temperature temperature comparison comparison in pulsating in pulsating flow. flow.

Finally, thethe simulationsimulation results were used to illustrate the heat transfer phenomena that couldthat could not benot observed be observed in the in the experiment, experiment, and and the the influence influence mechanism mechanism of of pulsating pulsating flow onflow the on heat the heat transfer transfer process process was was explained explained in detail.in detail. As shown in Figure 18,18, the instantaneous streamwise streamwise velocity velocity vector vectorss and and tempera- temperature contoursture contours of the of the horizontal horizontal section section along along thethe center axis axis in in the the curved curved pipe pipe were were used used toto reveal reveal the the heat heat transfer transfer mechanism mechanism in the in pulsating the pulsating flow. Figure flow. 18a Figure,b show 18sa,b the showsveloc- the velocityity vector vector and temperature and temperature contour contour of the steady of the steadyflow at flowthe curved at the part curved of the part pipe, of the re- pipe, respectively.spectively. They They were were used used for for comparison comparison with with pulsa pulsatingting flow flow situations. situations. The Thevelocity velocity vectorvector and temperature contour contour during during the the deceleration deceleration phase phase of the of thepulsating pulsating flow flowis as is as shownshown in Figure Figure 18c 18c,d,,d, respectively. respectively. The The separation separation between between the theair and air andsolid solid wall wallin the in the deceleration phase is larger than that in the steady flow. The air temperature was low in deceleration phase is larger than that in the steady flow. The air temperature was low in the the separation region, which reduced the temperature difference between the wall and separation region, which reduced the temperature difference between the wall and ambient ambient temperatures. Thus, the heat flux was reduced in this region. The large separation temperatures. Thus, the heat flux was reduced in this region. The large separation in the in the deceleration resulted in the suppression of heat transfer downstream of the curved deceleration resulted in the suppression of heat transfer downstream of the curved part. part. For a steady flow in a curved pipe, the impingement of the high-temperature core can enhance the heat transfer, as shown in Figure 18b. However, for the pulsating flow, the temperature changed periodically. Owing to the compressibility of air, a high-temper- ature air region appeared in the acceleration phase, and a low-temperature air region ap- peared in the deceleration phase. Figure 18e,f shows the velocity vector and temperature contour, respectively, during the deceleration phase of the pulsating flow before the min- imum velocity. The flow impingement phenomenon of the low-temperature core reduced the outer wall temperature of the curved part of the pipe. The temperature difference be- tween the outer wall and ambient temperatures was reduced, and the heat transfer was suppressed in this region. Figure 18g,h shows the temperature and velocity contours of the reverse flow downstream of the curved pipe, respectively. Because the temperature of the reverse flow was low, the wall temperature was reduced sharply during the period when the reverse flow occurred. Therefore, the heat flux decreases in the region where there is a reverse flow. In general, the large separation, impingement of the low-tempera- ture core, and reverse flow were all behaviors of heat transfer suppression.

Energies 2021, 14, 3953 17 of 20 Energies 2021, 13, x FOR PEER REVIEW 18 of 22

FigureFigure 18. Instantaneous18. Instantaneous velocity velocity vectors vectors and and temperature temperature fields fields of the of horizontal the horizontal section section along along the center the center axis of axis the curvedof the pipecurved in the pipe simulation: in the simulation (a) and (: b(a)) areand results (b) are ofresults the steadyof the steady flow, (flow,c) and (c) ( dand) are (d) the are resultsthe results of the of the deceleration deceleration phase phase of the pulsating flow, (e) and (f) are results of the pulsating flow approaching the minimum velocity, (g,h) are results of the reverse flow.

Energies 2021, 14, 3953 18 of 20

For a steady flow in a curved pipe, the impingement of the high-temperature core can enhance the heat transfer, as shown in Figure 18b. However, for the pulsating flow, the temperature changed periodically. Owing to the compressibility of air, a high-temperature air region appeared in the acceleration phase, and a low-temperature air region appeared in the deceleration phase. Figure 18e,f shows the velocity vector and temperature contour, respectively, during the deceleration phase of the pulsating flow before the minimum ve- locity. The flow impingement phenomenon of the low-temperature core reduced the outer wall temperature of the curved part of the pipe. The temperature difference between the outer wall and ambient temperatures was reduced, and the heat transfer was suppressed in this region. Figure 18g,h shows the temperature and velocity contours of the reverse flow downstream of the curved pipe, respectively. Because the temperature of the reverse flow was low, the wall temperature was reduced sharply during the period when the reverse flow occurred. Therefore, the heat flux decreases in the region where there is a reverse flow. In general, the large separation, impingement of the low-temperature core, and reverse flow were all behaviors of heat transfer suppression.

5. Conclusions In this study, experiment and simulation of turbulent steady and pulsating flows were performed for straight and 90◦ curved square pipes. The velocity measurement at the “Outlet” verified the existence of reverse flow under a pulsating flow with a large velocity amplitude. In both the streamwise and circumferential directions, the results of temperature fields in the experiment reported the difference between the steady and pulsating flows in the straight and curved pipes. For the straight pipe, the average cross-section temperature of the steady flow decreased linearly and monotonically in the streamwise direction. The streamwise temperature of the pulsating flow decreased nonlinearly. For both the steady and pulsating flows in the 90◦ curved pipe, the temperature decreased significantly near the outlet of the curved part of the pipe. The secondary temperature distribution is formed with the formation of Dean vortices. The local heat flux of different cross-sections in the experiment provided quantitative results of the heat transfer. The local heat flux of the pulsating flow in a straight pipe exhibits a large variation in different cross-sections. The closer to the pulsation generator, the larger the temperature oscillation and the higher the heat transfer performance are. It has an extremely large local heat flux near the outlet of the curved part of the curved pipe. In the test section, for both the steady and pulsating flows, the total heat flux of the curved pipe was higher than that of the straight pipe. For both straight and curved pipes, the total heat flux of the steady flow was higher than that of the pulsating flow. The instantaneous velocity and temperature fields of the numerical simulation were employed to illustrate the heat transfer mechanism of the pulsating flow. The behaviors, such as the large separation between the air and pipe wall, impingement of the low- temperature core, and reverse flow, suppressed the heat transfer. The conclusions on the phenomena of pulsating flow can be used as a reference in the design and optimization of intake and exhaust manifolds.

Author Contributions: Conceptualization, K.N., H.H., M.K. (Masanobu Koutoku), R.Y., H.Y. and S.S.; methodology, G.G., Y.O., M.K. (Masaya Kamigaki) and Y.I.; software, G.G.; validation, G.G.; formal analysis, G.G. and M.K. (Masaya Kamigaki); investigation, G.G., M.K. (Masaya Kamigaki), and Y.I.; resources, H.H.; data curation, G.G.; writing—original draft preparation, G.G.; writing—review and editing, Y.O.; visualization, G.G.; supervision, K.N. and Y.O.; project administration, H.H.; funding acquisition, H.H. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Energies 2021, 14, 3953 19 of 20

Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to huge experiment and simulation results and the complexity of the data analysis process. Acknowledgments: Thanks to the Hoday from Editage Group (www.editage.com 25 May 2021) for editing a draft of this manuscript. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

A surface area [m2] Cp constant pressure specific [J/kg·K] D pipe inner diameter [mm] De Dean number G derivative of temperature [K/s] m flow mass [kg] N total points of each cross section Q heat flow rate [W] q heat flux [W/m2] R correlation coefficient Re Reynolds number Rc radius of curvature [mm] T temperature [K] Tmea Temperature measurement time [s] t time [s] U velocity [m/s] X streamwise coordinate Y horizontal coordinate Z vertical coordinate Greek Symbols λ heat conductivity [W/m·K] ρ density [kg/m3] ν kinematic viscosity [m2/s] α Womersley number ω angular frequency [rad/s] τ time constant of thermocouple Subscripts 1 thermocouple of 13 µm 2 thermocouple of 25 µm c cross section i inlet g fluid n nth point o outlet t total w wall x local position Superscripts ¯ time average value ˙ rate

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